561 is a Carmichael Number

Given a prime, Fermat's little theorem gives us a certain collection of congruences modulo the prime. The converse, if it were true, would say that the truth of those congruences implies the primality of the modulus. The problem is that this simply is not true. The composite moduli that are counterexamples are called Carmichael numbers. The smallest counterexample is 561, and in this video we prove that it is a Carmichael number. We also describe Korselt's biconditional criterion for Carmichael numbers without proof (the proof of which we are aware is a complicated one that depends on primitive roots). Like, subscribe, and share! To find out more about us: - Visit https://existsforall.com to check out our services - Get our Rigorous Elementary Mathematics books on Amazon: https://www.amazon.com/dp/B0DGDNK6TM?binding=paperback Copyright © Existsforall Academy Inc. All rights reserved.